Mathematical Sciences: Algebraic Structure of Quantum Groups

数学科学：量子群的代数结构

• 批准号: 9501484
• 负责人: Timothy Hodges
• 金额: $ 5万
• 依托单位: University of Cincinnati Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501484&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Structure; Quantum

This award supports research on the analysis of the algebraic structure of non-standard quantum groups. The specific aims of the project are: (1) To analyze in detail the algebraic structure of the Cremmer-Gervais quantum groups along the lines of previous work of Hodges and Levasseur on the standard and multi-parameter cases; (2) To study the structure of the associated Poisson groups and Lie bialgebras and to compare this with the structure of the associated quantum group; (3) To construct further families of non-standard quantum groups. This research is in the general area of ring theory. A ring is an algebraic object having both an addition and a multiplication defined on it. Although the additive operation satisfies the commutative law, the multiplicative operation is not required to do so. An example of a ring for which multiplication in not commutative is the collection of nxn matrices over the integers. The study of noncommutative rings has become an important part of algebra because of its increasing significance to other branches of mathematics and physics.

该奖项支持非标准量子群的代数结构分析研究。 本项目的具体目标是：（1）沿着Hodges和Levasseur以前在标准和多参数情况下的工作，详细分析Cremmer-Gervais量子群的代数结构：（2）研究相关Poisson群和李双代数的结构，并与相关量子群的结构进行比较;（3）进一步构造非标准量子群族。 这项研究是在环理论的一般领域。 环是一个代数对象，它同时定义了加法和乘法。虽然加法运算满足交换律，但乘法运算不需要这样做。 一个环的例子是整数上的n × n矩阵的集合，其中乘法是不可交换的。 非交换环的研究已经成为代数学的一个重要组成部分，因为它对数学和物理学的其他分支越来越重要。